Trapped neutral atoms are promising candidates for performing quantum computations since they have long decoherence times and can easily be interfaced with light for single-qubit operations and measurements. We propose a method for entangling a pair of indistinguishable neutral atoms stored in separated optical dipole traps. We model this trapping potential in one dimension as a pair of Gaussian wells that can be brought together for atoms to interact. The dynamics of this process depend on the symmetrizations of the atomic subsystems. By choosing the correct interaction time a controlled-phase gate can be designed. Adiabatic separation guarantees that the atoms end up in opposite traps. We provide both adiabatic and time-dependent numerical simulations of the entangling process. Additionally, we consider a novel method for creating entangled qubits via selective excitation of atoms in an optical dipole trap.